Ballistic random walks in random environment at low disorder

Details Ballistic random walks in random environment at low disorder Ballistic random walks in random environment at low disorder

2003-02-07

arxiv.org/abs/math/0302076v2

Annals of Probability 2004, Vol. 32, No. 4, 2996-3023

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000739 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000739

We consider random walks in a random environment of the type p_0+\gamma\xi_z, where p_0 denotes the transition probabilities of a stationary random walk on \BbbZ^d, to nearest neighbors, and \xi_z is an i.i.d. random perturbation. We give an explicit expansion, for small \gamma, of the asymptotic speed of the random walk under the annealed law, up to order 2. As an application, we construct, in dimension d\ge2, a walk which goes faster than the stationary walk under the mean environment.

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